cp's OEIS Frontend

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.

A101996 Primes of the form 8*k-1 such that 4*k-1, 16*k-1, 32*k-1 and 64*k-1 are also primes.

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%I A101996 #17 May 13 2024 02:14:17
%S A101996 359,107279,126839,253679,254279,508559,592199,681839,1214639,1621079,
%T A101996 2138399,2245319,3197399,3243239,3641999,3732479,3825359,3841919,
%U A101996 4090679,4276799,4315799,4490639,4556159,4714439,5335559,5731679
%N A101996 Primes of the form 8*k-1 such that 4*k-1, 16*k-1, 32*k-1 and 64*k-1 are also primes.
%H A101996 Amiram Eldar, <a href="/A101996/b101996.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..750 from Harvey P. Dale)
%F A101996 a(n) = 8*A101994(n) - 1 = 2*A101995(n) + 1. - _Amiram Eldar_, May 13 2024
%e A101996 4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719, 32*45-1 = 1439 and 64*45-1 = 2879 are primes, so 359 is a term.
%t A101996 8#-1&/@Select[Range[720000],AllTrue[{4,8,16,32,64}#-1,PrimeQ]&] (* _Harvey P. Dale_, Jan 17 2023 *)
%t A101996 Select[Table[2^Range[2,6] n-1,{n,750000}],AllTrue[#,PrimeQ]&][[;;,2]] (* _Harvey P. Dale_, Jun 03 2023 *)
%o A101996 (PARI) is(k) = if(k % 8 == 7, my(m = k\8 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1) && isprime(64*m-1), 0); \\ _Amiram Eldar_, May 13 2024
%Y A101996 Cf. A101789, A101994, A101995, A101997, A101998, A101999.
%Y A101996 Subsequence of A007522, A101792 and A101796.
%K A101996 easy,nonn
%O A101996 1,1
%A A101996 Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 23 2004
%E A101996 Corrected by _T. D. Noe_, Nov 15 2006