A161197 Smallest Honaker prime A033548 with digit sum prime(n), or 0 if no such prime exists.

0, 0, 131, 2221, 263, 1039, 2591, 2719, 4397, 57089, 79609, 479881, 2557967, 1299499, 8796629, 49979249, 349929779, 753987769, 1397989867, 8278487999, 16874789779, 69355889899, 199785963989, 1787899947299, 17678888878867

Offset: 1

Author

Lekraj Beedassy, Jun 06 2009

Keywords

• nonn
• base

Comments

From Robert G. Wilson v, Jun 08 2009: (Start)

If instead the sequence is the least Honaker prime which digit sum a(n) then the terms would begin:

0, 0, 0, 0, 131, 0, 2221, 2141, 0, 6301, 263, 0, 1039, 1049, 0, 457, 2591, 0, 2719, 2729, 0, 3559, 4397, 0, 17359, 17189, 0, 37783, 57089, 0, 79609, 174767, 0, 324799, 349919, 0, 479881, 479783, 0, 879673, 2557967, 0, 1299499, 5487497, 0, 5487697, 8796629, 0, 14657899, 23879489, 0, 47678893, 49979249, 0, 67669687, 139579499, 0, 176937979, 349929779, 0, 753987769, 753987779, 0, 1397989819, 1397778887, 0, 1397989867, ..., . (End)

a(26) <= 29678788858889. - Donovan Johnson, Dec 29 2013

Examples

			The digit sums of A033548(n) are 5,11,16,13,14,11,5,11,11,14,14,16,8,7,14,11,17,17...
The first occurrence of the primes 5,7,11,13,... is at n=1,14,2,.., so the sequence displays A033548(1), A033548(14), A033548(2),...
		

Crossrefs

Cf. A033548.

Programs

Mathematica

t = Table[0, {100}]; c = 1; p = 2; While[p < 35*10^8, a = Plus @@ IntegerDigits@ c; b = Plus @@ IntegerDigits@ p; If[a < 101 && a == b && t[[a]] == 0, t[[a]] = p; Print[{a, p}]]; c++; p = NextPrime@p]; t[[ # ]] & /@ Prime@ Range@ 19 (* Robert G. Wilson v, Jun 08 2009 *)

Formula

a(n) = min A033548(k): A007953(A033548(k)) = A000040(n). [R. J. Mathar, Jun 16 2009]

Extensions

a(12)-a(19) from Robert G. Wilson v, Jun 08 2009

Simplified definition, added examples - R. J. Mathar, Jun 16 2009

a(20)-a(24) from Donovan Johnson, May 03 2010

a(25) from Donovan Johnson, Dec 29 2013