A078959 Primes p such that the differences between the 5 consecutive primes starting with p are (6,2,6,4).
23, 53, 263, 1283, 2333, 5843, 6563, 14543, 19373, 32363, 41603, 48473, 49193, 51413, 75983, 88793, 106853, 113153, 115763, 138563, 150203, 160073, 163973, 204353, 223823, 229763, 246923, 284723, 319673, 326993, 337853, 338153, 357653, 433253, 443153, 460073, 460973
Offset: 1
Keywords
Examples
53 is a term since 53, 59 = 53 + 6, 61 = 53 + 8, 67 = 53 + 14 and 71 = 53 + 18 are consecutive primes.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
l = {}; For[n = 1, n < 10^5, n++, If[Prime[n] + 6 == Prime[n + 1] \[And] Prime[n] + 8 == Prime[n + 2] \[And] Prime[n] + 14 == Prime[n + 3] \[And] Prime[n] + 18 == Prime[n + 4], AppendTo[l, Prime[n]]]]; l (* Jake Foster, Oct 27 2008 *) Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {6,2,6,4} &][[;;, 1]] (* Amiram Eldar, Feb 22 2025 *) -
PARI
list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 6 && p3 - p2 == 2 && p4 - p3 == 6 && p5 - p4 == 4, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5);} \\ Amiram Eldar, Feb 22 2025
Formula
a(n) == 23 (mod 30). - Amiram Eldar, Feb 22 2025
Extensions
Edited by Dean Hickerson, Dec 20 2002
Comments