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Honaker primes
A prime pn such that the sum of digits of n and pn is the same. more

The first 600 Honaker primes :
131, 263, 457, 1039, 1049, 1091, 1301, 1361, 1433, 1571, 1913, 1933, 2141, 2221, 2273, 2441, 2591, 2663, 2707, 2719, 2729, 2803, 3067, 3137, 3229, 3433, 3559, 3631, 4091, 4153, 4357, 4397, 4703, 4723, 4903, 5009, 5507, 5701, 5711, 5741, 5801, 5843, 5927, 6301, 6311, 6343, 6353, 6553, 6563, 6653, 6737, 6827, 6971, 7013, 7213, 7283, 7411, 7481, 7523, 7741, 8011, 8821, 9103, 10247, 10429, 10559, 10711, 11071, 11173, 11251, 11353, 11701, 11731, 11821, 12277, 12347, 12613, 13007, 13037, 13127, 13217, 13297, 13327, 13339, 13367, 13417, 13457, 13933, 14159, 14437, 14447, 14843, 14923, 15173, 15193, 15263, 15671, 15761, 15803, 15913, 16073, 16193, 16273, 16451, 16661, 17159, 17189, 17317, 17359, 18013, 18041, 18307, 20533, 20543, 21523, 21617, 22189, 22277, 22613, 22807, 23059, 23531, 24019, 24091, 24733, 24841, 24971, 25219, 25229, 25339, 26119, 26189, 26209, 26309, 26339, 26731, 27059, 27091, 27277, 29023, 29101, 29131, 29243, 29423, 30071, 30091, 30253, 30293, 31177, 31391, 31517, 31567, 32009, 32029, 32059, 32191, 32261, 33493, 33533, 34171, 34259, 34471, 34543, 34703, 35027, 35129, 35149, 35227, 35327, 35537, 35617, 36217, 36307, 36433, 36523, 37019, 37039, 37049, 37117, 37463, 37493, 37717, 37783, 38011, 38711, 40361, 40427, 40627, 40637, 40763, 40823, 41131, 41141, 41333, 41491, 41801, 41851, 41941, 42323, 42373, 42509, 42727, 42737, 43543, 43781, 44221, 44417, 45119, 45181, 45191, 45821, 45833, 46147, 46237, 46723, 47017, 47147, 47293, 47491, 47623, 48109, 48119, 48247, 48463, 48473, 49031, 49411, 49531, 50047, 50119, 50417, 51131, 51203, 51263, 51421, 51473, 52051, 52543, 52553, 52691, 52733, 53309, 53407, 53437, 53591, 53881, 53923, 54013, 54217, 54617, 54727, 54941, 55049, 55207, 55541, 55733, 55823, 56807, 57059, 57089, 57119, 57139, 57271, 57301, 57713, 57943, 58073, 58321, 58411, 58921, 59083, 59093, 59183, 60251, 60601, 61051, 61253, 61703, 62017, 62057, 62273, 62303, 62323, 62617, 62627, 63031, 63313, 63607, 64123, 64151, 64231, 64513, 64621, 64817, 65371, 65713, 65831, 65843, 66089, 66301, 66923, 67073, 67801, 68059, 68147, 68813, 68903, 69127, 69247, 69257, 69383, 69463, 69911, 70039, 70079, 70139, 70379, 70459, 70489, 71261, 71353, 72019, 72337, 72701, 73009, 73607, 74231, 74713, 75503, 75941, 76129, 76159, 76403, 76423, 77023, 77237, 77249, 77291, 77339, 77611, 77711, 77813, 78007, 78017, 78163, 78283, 78427, 78437, 79133, 79273, 79333, 79609, 80657, 81199, 81239, 82051, 82207, 82217, 82813, 83231, 83311, 84017, 84067, 84313, 85081, 85093, 85133, 86113, 86243, 87013, 87071, 87121, 87151, 88007, 88661, 89833, 90163, 90173, 90469, 90647, 91009, 91019, 91571, 91583, 92251, 92347, 92461, 92627, 92791, 92861, 93097, 94033, 94063, 94151, 94219, 94229, 94327, 95111, 95219, 96043, 96053, 96443, 96553, 97103, 97151, 97231, 97241, 97711, 98911, 99041, 100279, 100549, 100559, 100957, 101869, 101929, 101939, 102359, 102397, 102829, 103619, 103969, 103979, 105031, 105331, 106031, 106621, 106903, 108037, 109103, 109133, 109321, 109331, 110119, 110129, 110273, 110813, 110923, 111053, 111229, 111347, 111443, 111491, 112153, 112163, 112927, 113027, 113327, 113357, 113417, 113591, 113891, 114451, 114809, 115561, 115571, 115601, 115631, 115853, 116089, 116159, 116189, 116257, 117503, 118411, 120181, 120473, 120511, 120709, 120943, 122471, 122503, 122533, 123091, 123217, 123701, 123733, 123821, 124153, 124183, 124193, 124363, 124429, 124459, 125029, 125117, 125383, 125423, 125453, 125627, 126013, 126143, 126271, 126517, 126653, 126691, 127051, 127423, 127681, 127733, 127763, 129113, 129221, 130087, 130183, 131009, 131213, 131371, 131381, 132233, 132283, 132313, 132383, 132541, 132607, 132721, 132751, 132763, 133153, 133213, 133241, 133261, 133271, 133451, 133801, 133811, 133831, 134731, 134741, 135731, 136139, 136177, 136207, 136217, 136237, 136247, 136277, 136337, 136531, 136621, 137437, 138113, 138241, 138319, 139123, 139133, 139201, 139409, 139703, 139831, 140143, 140411, 140423, 140453, 141161, 141241, 141301, 141623, 142231, 142403, 143291, 143357, 143443, 143483, 144307, 145063, 145121, 145207, 145441, 145451, 145513, 145543, 145603, 145661, 145721, 145771, 146323, 147047, 149113, 149173, 149183, 149251, 150197, 150287, 151337, 151537, 151597, 151609, 152003, 152123, 152851, 154073, 154211, 154321, 155017, 155027, 155203, 156127, 156253, 156361.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 1478015 values, from 131 to 999843421).

n\r 0  1 
201478015 2 
30739402738613 3 
407371740740841 4 
50452116328347421923275629 5 
60739402000738613 6 
70246207246220245781246684246588246535 7 
80370172037056103670020370280 8 
9024628424578602469492460750246169246752 9 
10045211604219230003283470275629 10 
110147788148000148237147287147967148084147628147457147852147715

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.