A120819 Indices of primes in A057137.

171, 277, 367, 561, 567, 18881

Offset: 1

Author

Robert G. Wilson v, Jul 05 2006

Keywords

• nonn
• base
• hard
• more

Comments

Digits are in ascending order beginning with 1 and after 9 comes 0.

Indices of primes in A057137.

All terms must end in 1 or 7: A057137(n) is even when n is even, and divisible by 3 iff n == 0, 2, 3, 5, 6, 8 or 9 (mod 10). - M. F. Hasler, Apr 14 2024

a(7) >= 100000. - Michael S. Branicky, Apr 07 2025

Examples

			a(1) = 12345678901234567890...01234567890...012345678901 = A057137(171) is the first prime term in A057137.
		

References

• Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61, 298.

Crossrefs

Cf. A006055, A057137, A120828, A120820, A120821, A120822, A120823, A120824, A120825, A120826, A120827.

Programs

Mathematica

fQ[n_] := PrimeQ@ FromDigits@ Mod[Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst
IntegerLength[Select[Table[FromDigits[PadRight[{},n,{1,2,3,4,5,6,7,8,9,0}]],{n,1,1001,2}],PrimeQ]] (* Harvey P. Dale, Feb 07 2024 *)

PARI

N=0;for(n=1,600,if(ispseudoprime(N=10*N+n%10),print1(n", "))) \\ Charles R Greathouse IV, May 10 2014  (Comment: Surprisingly, this is faster than calling ispseudoprime() only when n ends in 1 or 7, even when much larger N's are considered, e.g., up to 3000. - M. F. Hasler, Apr 14 2024)

Python

from sympy import isprime
L = ['8901', '234567']; s = '1234567'; c = len(s); m = 0
while c < 18881:
    s += L[m%2]; c = len(s); m += 1
    if isprime(int(s)): print(c, end = ', ')  # Ya-Ping Lu, Jan 24 2025

Extensions

a(6) from Arjen Lenstra, Feb 20 2012