

A129990


Primes p such that the smallest integer whose sum of decimal digits is p is prime.


0



2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 71, 79, 97, 173, 179, 257, 269, 311, 389, 691, 4957, 8423, 11801, 14621, 25621, 26951, 38993, 75743, 102031, 191671, 668869
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..33.


FORMULA

Primes p such that (p mod 9 + 1) * 10^[p/9]  1 is prime. Therefore the sequence consists of primes of the forms A002957(k)*9+1, A056703(k)*9+2, A056712(k)*9+4, A056716(k)*9+5, A056721(k)*9+7, A056725(k)*9+8. [From Max Alekseyev]


EXAMPLE

The smallest integer whose sum of digits is 17 is 89; 89 is prime, therefore 17 is in the sequence.


MATHEMATICA

Select[Prime[Range[1000]], PrimeQ[FromDigits[Join[{Mod[ #, 9]}, Table[9, {i, 1, Floor[ #/9]}]]]] &]


CROSSREFS

Cf. A051885.
Sequence in context: A108543 A042988 A167135 * A301590 A293194 A162566
Adjacent sequences: A129987 A129988 A129989 * A129991 A129992 A129993


KEYWORD

hard,more,nonn,base


AUTHOR

J. M. Bergot, Jun 14 2007


EXTENSIONS

Edited, corrected and extended by Stefan Steinerberger, Jun 23 2007
Extended by D. S. McNeil, Mar 20 2009
Five more terms from Max Alekseyev, Nov 09 2009


STATUS

approved



