| Displaying 1-7 of 7 results found.
page
1
Primes such that the absolute value of the difference between the largest digit and the sum of all the other digits is a cube.
+10
2
11, 19, 23, 43, 67, 89, 101, 109, 113, 131, 157, 167, 179, 197, 199, 211, 223, 241, 257, 263, 269, 311, 313, 331, 337, 347, 353, 359, 373, 379, 397, 421, 431, 449, 461, 463, 523, 541, 571, 593, 607, 617, 641, 643, 661, 683, 719, 733, 739, 743
COMMENTS
If the largest digit L (say) is repeated, the criterion is that |L - (sum of all digits except for one copy of L)| is a cube.
EXAMPLE
The prime 2731 is a term, because 7-2-3-1 = 1 is a cube.
The prime 13 is not in the sequence, as 3-1 = 2, and 2 is not a cube.
The prime 313 is a term because |3 - (1+3)| = 1 is a cube.
MATHEMATICA
Select[Prime[Range[150]], IntegerQ[Surd[Abs[Max[IntegerDigits[#]]-Total[ Most[ Sort[IntegerDigits[#]]]]], 3]]&] (* Harvey P. Dale, Dec 31 2021 *)
PROG
(PARI) listA280993(k, {k0=5})={my(H=List(), y); forprime(z=prime(k0), prime(k), y=digits(z); if(ispower(abs(vecsum(y)-2*vecmax(y)), 3), listput(H, z))); return(vector(#H, i, H[i]))} \\ Looks for those belonging terms between prime(k0) and prime(k). - R. J. Cano, Feb 06 2017
Prime numbers p such that prime = abs(smallest digit of p - sum of all the other digits of p).
+10
1
2, 3, 5, 7, 13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 101, 113, 131, 139, 151, 157, 193, 199, 211, 223, 227, 241, 263, 269, 311, 313, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 463, 487, 557, 571, 593, 599, 601, 607, 643, 661, 683, 733, 739, 751, 773
EXAMPLE
13(2=abs(1-3)), 29(7=abs(2-9)), 31(2=3-1)
MATHEMATICA
sdsodQ[n_]:=Module[{sidn=Sort[IntegerDigits[n]]}, PrimeQ[Abs[sidn[[1]]-Total[Rest[sidn]]]]]; Select[Prime[Range[150]], sdsodQ] (* Harvey P. Dale, Feb 01 2015 *)
EXTENSIONS
Single-digit primes added, duplicates of 421 and 443 removed - R. J. Mathar, May 19 2010
Prime numbers p such that 1 = abs(final digit of p - sum of all the other digits of p).
+10
1
23, 43, 67, 89, 113, 157, 179, 199, 223, 269, 313, 337, 359, 379, 449, 607, 719, 739, 809, 829, 919, 1013, 1033, 1103, 1123, 1213, 1237, 1259, 1279, 1303, 1327, 1439, 1459, 1549, 1619, 1709, 2003, 2069, 2089, 2113, 2137, 2179, 2203, 2269, 2339, 2539
EXAMPLE
23(1=3-2), 43(1=abs(3-4)), 67(1=abs(7-6)), 89(1=abs(9-8)), 113(1=3-(1+1)).
MATHEMATICA
ps1[n_]:=Module[{idn=IntegerDigits[n]}, Abs[Last[idn]-Total[Most[idn]]] == 1]; Select[Prime[Range[400]], ps1] (* Harvey P. Dale, Jul 31 2012 *)
Primes p such that 2 = abs(largest digit of p - sum of all the other digits of p).
+10
0
2, 13, 31, 53, 79, 97, 103, 163, 233, 251, 277, 349, 367, 383, 389, 433, 439, 457, 479, 503, 521, 547, 563, 569, 613, 619, 631, 653, 659, 673, 691, 709, 727, 839, 907, 929, 947, 983, 1063, 1069, 1151, 1223, 1249, 1283, 1289, 1423, 1429, 1447, 1481, 1511
Primes p such that 3 = abs(largest digit of p - sum of all the other digits of p).
+10
0
3, 41, 47, 137, 151, 173, 227, 283, 317, 401, 443, 467, 487, 557, 647, 773, 823, 883, 1051, 1217, 1277, 1307, 1367, 1381, 1433, 1453, 1543, 1637, 1721, 1783, 1831, 1873, 2027, 2083, 2207, 2221, 2243, 2267, 2281, 2287, 2357, 2423, 2441, 2447, 2551, 2683
COMMENTS
Since zero digits are allowed, sequence is almost certainly infinite. - Zak Seidov, Feb 22 2009
EXAMPLE
a(1)=3 because 3=abs(3-0). a(4)=137 because 1<3<7 and 3=abs(7-(1+3)).
MATHEMATICA
moQ[n_]:=Module[{idn=IntegerDigits[n]}, Abs[2Max[idn]-Total[idn]] ==3]; Select[Prime[Range[500]], moQ] (* Harvey P. Dale, May 12 2011 *)
Composite numbers k such that prime = abs(smallest digit of k - sum of all the other digits of k).
+10
0
14, 16, 18, 20, 24, 25, 27, 30, 35, 36, 38, 42, 46, 49, 50, 52, 57, 58, 63, 64, 68, 69, 70, 72, 74, 75, 81, 85, 86, 92, 94, 96, 102, 104, 106, 110, 112, 115, 117, 120, 121, 122, 124, 126, 133, 135, 140, 142, 144, 148, 153, 159, 160, 162, 166, 168, 171, 175, 177, 184
EXAMPLE
14(3=abs(1-4)), 16(5=abs(1-6)), 18(7=abs(1-8)), 20(2=2-0)
MATHEMATICA
sdkQ[n_]:=Module[{id=IntegerDigits[n], mid}, mid=Min[id]; PrimeQ[Abs[mid-Total[DeleteCases[ id, mid, 1, 1]]]]]; cnkQ[n_]:=CompositeQ[n]&&sdkQ[n]; Select[Range[200], cnkQ] (* Harvey P. Dale, Aug 23 2024 *)
Primes p whose decimal representation satisfy: abs(digsum(p)-2*L(p)) = 8, being L(p) the largest decimal digit in p.
+10
0
19, 109, 1009, 1777, 1889, 1979, 1997, 2677, 2699, 2767, 2789, 2879, 2897, 2969, 3779, 3797, 4567, 4657, 4679, 4967, 5399, 5557, 5647, 5669, 5737, 5849, 5939, 6277, 6299, 6367, 6389, 6547, 6563, 6569, 6637, 6653, 6659, 6673, 6763, 6947, 6983, 7177
EXAMPLE
a(4) = 1777, since abs(digsum(1777)-2*L(1777)) = abs( A007953(1777)-2* A054055(1777)) is 8 and among the primes 1777 is the 4th element satisfying such condition.
MATHEMATICA
Select[Prime@ Range[10^3], Abs[Max@ # - Total@ Rest@ #] == 8 &@ Reverse@ Sort@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 02 2017 *)
PROG
(PARI) listA281170(k, {k0=8})={my(H=List(), y); forprime(z=prime(k0), prime(k), y=digits(z); if(abs(vecsum(y)-2*vecmax(y))==8, listput(H, z))); return(vector(#H, i, H[i]))} \\ Looks for those belonging terms between prime(k0) and prime(k). - R. J. Cano, Feb 06 2017
Search completed in 0.005 seconds
|