The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309720 Numbers of the form p+q-r = q+r-s where p < q < r < s are consecutive primes. 1
 1, 13, 37, 65, 223, 343, 637, 1087, 1273, 1423, 1445, 1483, 1603, 1687, 1867, 2077, 2135, 2375, 2605, 2683, 2705, 3029, 3523, 3545, 3913, 3997, 4123, 4633, 4783, 4927, 5435, 5735, 6079, 7205, 7295, 7331, 7547, 7589, 7811, 8159, 8227, 8701, 8827, 9085, 9335, 9457, 9461, 9923, 10057 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The consecutive primes (p,q,r,s) satisfy 2*(r-p) = s-p. Define (p,q,r,s) = (p,p+dq,p+dr,p+ds), then 2*dr = ds. For n > 1, (r-p) == 0 (mod 6). - A.H.M. Smeets, Aug 17 2019 Correspond to where prime(i) - (prime(i+2)-prime(i+1)) values repeat. For example, 13 is obtained via both 19 - (29-23) and 17 - (23-19). - Bill McEachen, Jan 03 2021 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE Consider 4 consecutive primes (3,5,7,11), 3+5-7 = 1 = 5+7-11. 1 is a member of the sequence. Consider 4 consecutive primes (59,61,67,71), 59+61-67 = 53 but, 61+67-71 = 57. These two sums are not equal so neither number is part of the sequence. MATHEMATICA upto[n_]:=Block[{p, q, r, s, t, v}, Union[ Reap[ Do[ {p, q, r, s}=t; v=p+q-r; If[ v==q+r-s <= n, Sow@ v], {t, Partition[ Prime[ Range[ 4+ PrimePi[ 2*n] ]], 4, 1]}]] [[2, 1]]]]; upto[11000] (* Giovanni Resta, Sep 06 2019 *) #[[1]]+#[[2]]-#[[3]]&/@Select[Partition[Prime[Range[2000]], 4, 1], #[[1]]+#[[2]]- #[[3]] == #[[2]]+#[[3]]-#[[4]]&] (* Harvey P. Dale, Sep 21 2022 *) CROSSREFS Cf. A096379, A138042. Cf. A066495. Sequence in context: A307192 A147207 A146877 * A233435 A049742 A347209 Adjacent sequences: A309717 A309718 A309719 * A309721 A309722 A309723 KEYWORD nonn AUTHOR Philip Mizzi, Aug 14 2019 EXTENSIONS More terms from Michel Marcus, Aug 14 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 13:56 EST 2022. Contains 358534 sequences. (Running on oeis4.)