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A329164 Let P1, P2, P3, P4 be consecutive primes, with P2-P1=P4-P3=2. a(n)=(P1+P2)/12 when P3-P2 sets a new record. 7
1, 23, 322, 495, 3407, 8113, 28893, 139708, 716182, 2497092, 5130198, 5761777, 7315173, 13194622, 145995245, 201544467, 417649822, 566513637, 833667068, 2266818768, 4710228962, 5186737183, 5192311957, 7454170028, 9853412390, 11817808908 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Position of record gaps with no primes bounded by consecutive pairs of twin primes. The length of the corresponding record gaps (P3-P1)/6 is given by A329165.
LINKS
Tomáš Brada and Natalia Makarova, Table of n, a(n) for n = 1..58
EXAMPLE
Values of P1, P2, P3, P4 corresponding to record gaps:
P3-P1 P1 P2 P3 P4 a(n)
6 5 7 11 13 (5+7)/12 = 1
12 137 139 149 151 (137+139)/12 = 23
18 1931 1933 1949 1951 (1931+1933)/12 = 322
30 2969 2971 2999 3001 (2969+2971)/12 = 495
PROG
(PARI) p1=3; p2=5; p3=7; r=0; forprime(p4=11, 1e9, if(p2-p1==2&&p4-p3==2, d=p3-p2; if(d>r, r=d; print1((p1+p2)/12, ", "))); p1=p2; p2=p3; p3=p4)
CROSSREFS
Sequence in context: A142433 A234234 A125458 * A329250 A022747 A270498
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Nov 07 2019
STATUS
approved

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Last modified July 13 20:42 EDT 2024. Contains 374288 sequences. (Running on oeis4.)