A129990 Primes p such that the smallest integer whose sum of decimal digits is p is prime.

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

Offset: 1

Author

J. M. Bergot, Jun 14 2007

Keywords

• hard
• more
• nonn
• base

Examples

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

Crossrefs

Cf. A051885.

Cf. A002957, A056703, A056712, A056716, A056721, A056725.

Programs

Mathematica

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

Python

from itertools import islice
from sympy import isprime, nextprime
def A051885(n): return ((n%9)+1)*10**(n//9)-1 # from Chai Wah Wu
def agen(startp=2):
    p = startp
    while True:
        if isprime(A051885(p)): yield p
        p = nextprime(p)
print(list(islice(agen(), 23))) # Michael S. Branicky, Jul 27 2022

Sage

sorted( filter(is_prime, sum(([9*t+k for t in oeis(seq).first_terms()] for seq,k in (('A002957',1), ('A056703',2), ('A056712',4), ('A056716',5), ('A056721',7), ('A056725',8))), [3])) ) # Max Alekseyev, Feb 05 2025

Formula

Primes p such that (p mod 9 + 1) * 10^[p/9] - 1 is prime. Therefore the sequence consists of the term 3 and the 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. - Max Alekseyev, Nov 09 2009

Extensions

Edited, corrected and extended by Stefan Steinerberger, Jun 23 2007

Extended by D. S. McNeil, Mar 20 2009

a(29)-a(33) from Max Alekseyev, Nov 09 2009