A389092 Pythagorean prime shift, variant: fully multiplicative with a(2) = 3, a(A002144(n)) = A002144(1+n) and a(A002145(n)) = a(A002145(1+n)) for all n >= 1, where A002144 and A002145 give the primes of the form 4k+1 and 4k+3 respectively.

1, 3, 7, 9, 13, 21, 11, 27, 49, 39, 19, 63, 17, 33, 91, 81, 29, 147, 23, 117, 77, 57, 31, 189, 169, 51, 343, 99, 37, 273, 43, 243, 133, 87, 143, 441, 41, 69, 119, 351, 53, 231, 47, 171, 637, 93, 59, 567, 121, 507, 203, 153, 61, 1029, 247, 297, 161, 111, 67, 819, 73, 129, 539, 729, 221, 399, 71, 261, 217, 429, 79

Offset

1,2

Comments

Contains only odd multiples of non-multiples of 5.

In contrast to many other prime shifts (like A003961 and A332818), iterating this sequence, whether starting from p=2 or p=5 does not generate all odd primes, but only either A002144\{5} or A002145.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Prog

(PARI) A389092(n) = { my(f=factor(n)); for(k=1, #f~, if(2==f[k, 1], f[k, 1]=3, for(i=1+primepi(f[k, 1]), oo, if(2==((f[k, 1]+prime(i))%4), f[k, 1]=prime(i); break)))); factorback(f); };

Crossrefs

Permutation of A045572.

Cf. A002144, A002145.

Cf. also A003961, A332818, A348746, A354091, A354202 for similar maps.

Sequence in context: A215800 A103601 A291344 * A297002 A111250 A118643

Adjacent sequences: A389089 A389090 A389091 * A389093 A389094 A389095

Keyword

nonn,mult

Author

Antti Karttunen, Sep 24 2025

Status

approved