cp's OEIS Frontend

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

%I A349622 #11 Nov 27 2021 11:04:29
%S A349622 1,2,3,7,19,25,26,31,33,37,79,93,97,139,157,199,211,229,271,307,331,
%T A349622 337,367,379,439,499,547,577,601,607,619,661,691,727,811,829,841,877,
%U A349622 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
%N A349622 Numbers k for which 2k-1 can be obtained with successive prime shifts towards larger primes (by iterating A003961, starting from k).
%C A349622 Numbers k for which A246277(2k-1) = A246277(k). This in turn implies a looser condition A046523(2k-1) = A046523(k).
%C A349622 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.
%H A349622 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A349622 (PARI)
%o A349622 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);
%o A349622 isA349622(n) = (A246277(n)==A246277(n+n-1));
%Y A349622 Subsequences: A005382 (primes present), A048674 (terms requiring only one iteration to reach 2k-1).
%Y A349622 Cf. A003961, A046523, A246277.
%Y A349622 Cf. also A348511.
%K A349622 nonn
%O A349622 1,2
%A A349622 _Antti Karttunen_, Nov 26 2021