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A253717 Primes equal to their partial cyclical digital sum numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A003459 A276132 A202264 * A186307 A321420 A118725

Adjacent sequences:  A253714 A253715 A253716 * A253718 A253719 A253720

KEYWORD

nonn,base

AUTHOR

V.J. Pohjola, May 02 2015

STATUS

approved

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Last modified April 19 11:46 EDT 2021. Contains 343114 sequences. (Running on oeis4.)