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
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.
Programs
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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
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