This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383650 #19 May 06 2025 11:51:17 %S A383650 4,6,12,18,30,60,72,108,138,192,240,270,312,348,420,432,570,642,810, %T A383650 822,828,1020,1050,1092,1302,1320,1452,1620,1668,1698,1722,1950,1998, %U A383650 2310,2550,2688,2712,2730,2970,3000,3168,3258,3330,3372,3462,3468,3540,3582,4092 %N A383650 Averages k of a twin prime pair such that 3*k*2^d is also the average of a twin prime pair for some divisor d of 3*k. %C A383650 All terms after a(2) are abundant (A005101), this is because all primes greater than 3 are of the form 6*k +- 1, thus the average of twin primes is 6*k, and since any multiple of a perfect or abundant number is abundant itself, it means that this property holds for all n > 11. - _Jakub Buczak_, May 04 2025 %H A383650 Jakub Buczak, <a href="/A383650/b383650.txt">Table of n, a(n) for n = 1..125</a> %F A383650 a(n) ~ b*n^c for some constants b and c as n tends to infinity (conjectured). - _Jakub Buczak_, May 04 2025 %e A383650 Average 4 of a twin prime pair is in the sequence because 3*4*2^4 = 192 is also the average of twin primes 191 and 193 for divisor d = 4 of 3*k = 3*4 = 12. %o A383650 (Magma) [k: k in [4..4100] | not #[d: d in Divisors(3*k) | IsPrime(k-1) and IsPrime(k+1) and IsPrime(3*k*2^d-1) and IsPrime(3*k*2^d+1)] eq 0]; %Y A383650 Supersequence of A014574. %Y A383650 Cf. A000040, A383475, A005101, A173490. %K A383650 nonn %O A383650 1,1 %A A383650 _Juri-Stepan Gerasimov_, May 04 2025 %E A383650 More terms from _Jakub Buczak_, May 04 2025