A349622 Numbers k for which 2k-1 can be obtained with successive prime shifts towards larger primes (by iterating A003961, starting from k).

1, 2, 3, 7, 19, 25, 26, 31, 33, 37, 79, 93, 97, 139, 157, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 661, 691, 727, 811, 829, 841, 877, 937, 967, 979, 997, 1009, 1034, 1069, 1171, 1237, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1657, 1759, 1867, 2011, 2029, 2089, 2131, 2137

Offset: 1

Author

Antti Karttunen, Nov 26 2021

Keywords

• nonn

Comments

Numbers k for which A246277(2k-1) = A246277(k). This in turn implies a looser condition A046523(2k-1) = A046523(k).

Nonsquarefree terms are rare: 25, 841 (= 29^2), 970225 ( = 5^2 * 197^2), ..., also 414690595, which is not a square. Some of these are also terms of A048674. Compare to A348511.

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Subsequences: A005382 (primes present), A048674 (terms requiring only one iteration to reach 2k-1).

Cf. A003961, A046523, A246277.

Cf. also A348511.

Programs

PARI

A246277(n) = if(1==n, 0, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f)/2);
isA349622(n) = (A246277(n)==A246277(n+n-1));