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a(n) = a(n-1) + rotate( a(n-1), 1 digit right), a(1) = 1.
+10
6
1, 2, 4, 8, 16, 77, 154, 569, 1525, 6677, 14344, 55778, 141355, 655490, 721039, 1693142, 3862456, 10248701, 21273571, 33400928, 116741020, 128415122, 341256634, 775382297, 1552920526, 7708212578, 16479033835, 68126937218, 154939630939, 1070433594032
MATHEMATICA
NestList[#+FromDigits[RotateRight[IntegerDigits[#]]]&, 1, 30] (* Harvey P. Dale, Dec 27 2021 *)
AUTHOR
Armand Turpel armandt(AT)unforgettable.com
a(n) = a(n-1) + rotate(a(n-1), n-1 digits left) with a(1) = 1.
+10
4
1, 2, 4, 8, 16, 77, 154, 695, 1264, 3905, 4444, 8888, 17776, 93953, 133348, 481481, 1296295, 7591424, 11839015, 50854133, 92189218, 114081407, 928152547, 1182945362, 10636566544, 47203110650, 78309615370, 139846693679, 606783485077, 955291245755, 1201047201046
EXAMPLE
Here we use -m (where m > 0) to represent rotating the digits of a number m digits to the left.
a(9) = a(8) + rotate(a(8), -8) = 695 + rotate(695, -8) = 695 + 569 = 1264.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateLeft[IntegerDigits[a[n - 1]], n - 1]; arr = a[#] & /@ Range[1, 100]
nxt[{n_, a_}]:={n+1, a+FromDigits[RotateLeft[IntegerDigits[a], n]]}; NestList[nxt, {1, 1}, 30][[;; , 2]] (* Harvey P. Dale, Nov 08 2024 *)
a(n) = a(n-1) + rotate(a(n-1), n-2 digits right) with a(1) = 1.
+10
3
1, 2, 4, 8, 16, 32, 55, 110, 121, 332, 664, 1130, 2431, 4862, 7348, 12221, 24442, 46886, 133354, 266708, 1093378, 2027159, 4054318, 12459749, 37057240, 74114480, 81525928, 110341187, 220682374, 642750611, 759178117, 876937295, 1606524988, 10422590237, 20845180474, 62929698521, 84558995506
EXAMPLE
a(12) = a(11) + rotate(a(11), 11) = 1130 + rotate(1130, 11) = 1130 + 1301 = 2431.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateRight[IntegerDigits[a[n - 1]], n - 2]; arr = a[#] & /@ Range[0, 100]
a(n) = a(n-1) + rotate(a(n-1), n-1 digits right) with a(1) = 1.
+10
3
1, 2, 4, 8, 16, 77, 154, 569, 1264, 5390, 14443, 45887, 133345, 646679, 1443145, 6587459, 12553333, 43808666, 110246752, 321271427, 594484141, 736078625, 1598652232, 3920250884, 4804642909, 9095590955, 15005150050, 65055300101, 95065465156, 149717034662
EXAMPLE
a(12) = a(11) + rotate(a(11), 11) = 14443 + rotate(14443, 11) = 14443 + 31444 = 45887.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateRight[IntegerDigits[a[n - 1]], n - 1]; arr = a[#] & /@ Range[1, 100]
a(n) = a(n-1) + rotate(a(n-1), n-2 digits left) with a(1) = 1.
+10
3
1, 2, 4, 8, 16, 32, 55, 110, 211, 332, 664, 1310, 1441, 2882, 11704, 52874, 105748, 586805, 1145485, 5996630, 9056596, 15962255, 41478217, 58892999, 154782298, 452937080, 1257466450, 7707592196, 9675299788, 18572052785, 46423909990, 145470333899, 484461788602
EXAMPLE
a(13) = a(12) + rotate_left(a(12), 11) = 1310 + rotate_left(1310, 11) = 1310 + 0131 = 1441.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = a[n - 1] + FromDigits@RotateLeft[IntegerDigits[a[n - 1]], n - 2]; arr = a[#] & /@ Range[1, 100]
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