A343158 a(n) is the smallest m such that A343156(m) = n, or -1 if no such m exists.

2, 4, 10, 35, 15, 34, 190, 290, 303, 395, 130, 465, 553, 265, 195, 663, 218, 582, 481, 858, 714, 418, 345, 530, 382, 1771, 1207, 2098, 3890, 1426, 2090, 4834, 4618, 627, 2321, 2163, 326, 866, 3302, 1298, 3886, 3094, 1086, 6130, 4807, 3646, 5181, 905, 3945, 5753

Offset: 0

Author

N. J. A. Sloane, Apr 07 2021

Keywords

• nonn
• base

Examples

			2 takes 0 steps to reach a prime, so a(0) = 2.
10 -> 25 -> 5 takes 2 steps to reach a prime (and no smaller number takes that many steps), so a(2) = 10.
35 -> 57 -> 319 -> 1129 takes 3 steps to reach a prime (and no smaller number takes that many steps), so a(3) = 35.
		

References

• Eric Angelini, W. Edwin Clark, Hans Havermann, Frank Stevenson, Allan C. Wechsler, and others, Postings to Math Fun mailing list, April 2021.

Crossrefs

Cf. A084317, A084319, A343156.

Programs

PARI

is(m, n) = my(k=m); for(i=1, n, if(isprime(k), return(0), k=eval(concat(apply(t->Str(t), factor(k)[, 1]~))))); isprime(k);
a(n) = for(m=2, oo, if(is(m, n), return(m))); \\ Jinyuan Wang, Jul 16 2022

Extensions

a(32)-a(42) from Hans Havermann, Apr 07 2021

a(43)-a(48) from Hans Havermann, Apr 08 2021

a(49) from Jinyuan Wang, Jul 16 2022