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

Author

V.J. Pohjola, May 02 2015

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A257275.

Cf. A106039.

Programs

Haskell

a253717 n = a253717_list !! (n-1)
a253717_list = filter ((== 1) . a010051') a106039_list
-- Reinhard Zumkeller, May 07 2015

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]

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