A253717 Primes equal to their partial cyclical digital sum numbers.

2, 3, 5, 7, 11, 13, 17, 31, 53, 71, 101, 131, 157, 173, 181, 197, 211, 283, 431, 439, 457, 461, 487, 509, 571, 601, 643, 727, 911, 929, 1021, 1031, 1033, 1051, 1093, 1151, 1163, 1171, 1201, 1231, 1249, 1259, 1301, 1303, 1327, 1373, 1399, 1429, 1451, 1453, 1493

Offset

1,1

Comments

Subsequence of primes of A106039. - Michel Marcus, May 03 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

Prime(37) = 157 = (1+5+7)*12 + 1.
Prime(40) = 173 = (1+7+3)*15 + 1+7.
Prime(42) = 181 = (1+8+1)*18 + 1.

Mathematica

terms = {}; (Do[p = Prime[n]; iD = IntegerDigits[p]; iD[[0]] = 0;
  a = Apply[Plus, iD]; pf = p - Mod[p, Floor[p/a]*a];
  (Do[pf = pf + Apply[Plus, iD[[i]]];
    If[pf == p, AppendTo[terms, pf]], {i, 0, IntegerLength[Prime[n]]}]), {n,
   1, 1000}]); Union[terms]

Prog

(PARI) isok(n) = {my(v = divrem(n, sumdigits(n))[2]); if (!v, return (1)); d = digits(n); for (i=1, #d, v -= d[i]; if (!v, return (1)); ); return (0); }
lista(nn) = forprime (n=1, nn, if (isok(n), print1(n, ", "))); \\ Michel Marcus, May 03 2015
(Haskell)
a253717 n = a253717_list !! (n-1)
a253717_list = filter ((== 1) . a010051') a106039_list
-- Reinhard Zumkeller, May 07 2015

Crossrefs

Cf. A257275.

Cf. A106039.

Sequence in context: A276132 A202264 A377266 * A186307 A321420 A118725

Adjacent sequences: A253714 A253715 A253716 * A253718 A253719 A253720

Keyword

nonn,base

Author

V.J. Pohjola, May 02 2015

Status

approved