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

Author

Giovanni Teofilatto, Jun 15 2010

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Different from A068807.

Programs

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 *)

Extensions

Corrected by Giovanni Teofilatto, Jun 25 2010

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