A178796 An ascending sequence of primes a(n) such that either the sum of decimal digits of a(n) is divisible by the sum of decimal digits of a(n+1) or vice versa.

2, 11, 13, 17, 31, 53, 71, 79, 97, 101, 103, 107, 211, 233, 251, 277, 349, 367, 431, 439, 457, 503, 521, 547, 619, 673, 691, 701, 709, 727, 853, 907, 1021, 1061, 1069, 1087, 1151, 1201, 1223, 1249, 1429, 1447, 1483, 1511, 1601, 1609, 1627, 1663, 1753, 1861, 1933, 1951, 2011, 2099

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The sums of the digits of a(n) form the sequence d(n) = 2, 2, 4, 8, 4, 8, 8, 16, ... in which either d(n)/d(n+1) or d(n+1)/d(n) is an integer.

Maple

A178796 := proc(n) option remember; if n = 1 then 2; else a := nextprime(procname(n-1)) ; while true do r := A007953(a)/ A007953(procname(n-1)) ; if numer(r) = 1 or denom(r) = 1 then return a; end if; a := nextprime(a) ; end do: end if; end proc:
seq(A178796(n), n=1..80) ; # R. J. Mathar, Jun 28 2010

Mathematica

nxt[n_]:=Module[{k=NextPrime[n], tidn=Total[IntegerDigits[n]]}, While[ !Divisible[ Total[ IntegerDigits[ k]], tidn] && !Divisible[ tidn, Total[ IntegerDigits[k]]], k=NextPrime[k]]; k]; NestList[nxt, 2, 60] (* Harvey P. Dale, Aug 23 2017 *)

Crossrefs

Different from A068807.

Sequence in context: A079132 A184802 A023257 * A068807 A241732 A154812

Adjacent sequences: A178793 A178794 A178795 * A178797 A178798 A178799

Keyword

base,nonn

Author

Giovanni Teofilatto, Jun 15 2010

Extensions

Corrected by Giovanni Teofilatto, Jun 25 2010

Definition corrected, sequence extended, example added by R. J. Mathar, Jun 28 2010

Status

approved