A056703 -id:A056703 - cp's OEIS frontend

A055559 Primes of the form 2999...999.

2, 29, 2999, 2999999, 29999999, 29999999999999999999, 2999999999999999999999999999, 29999999999999999999999999999999999999999999, 29999999999999999999999999999999999999999999999999999999

Offset: 1

Labos Elemer, Jul 10 2000

a(9)=29999999999999999999999999999999999999999999999999999999. - Vincenzo Librandi, Aug 07 2010

The next term (a(10)) has 208 digits, and a(11) has 1312 digits. - Harvey P. Dale, Jan 22 2023

			3*10^k - 1 is prime for k = 0, 1, 3, 6, 7, 19, ... (A056703). k gives the number of 9's in these numbers.

Cf. A051200, A056703, A056703.

Select[Table[FromDigits[PadRight[{2}, n, 9]], {n, 60}], PrimeQ] (* Harvey P. Dale, Jan 22 2023 *)

a(n) = A198698(A056703(n)) = 3*10^A056703(n) - 1. - Amiram Eldar, Mar 16 2025

Erroneous Formula entry removed by Jon E. Schoenfield, Jan 14 2018

Extended by Harvey P. Dale, Jan 22 2023

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

Original entry on oeis.org

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

J. M. Bergot, Jun 14 2007

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

Cf. A051885.

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

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

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

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

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

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

cp's OEIS Frontend

A055559 Primes of the form 2999...999.

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