A298466 The first of two consecutive primes the sum of which is equal to the sum of two consecutive heptagonal numbers.

3, 23, 433, 16481, 24593, 167953, 173183, 183871, 192097, 223781, 414521, 447743, 477857, 508951, 513473, 792983, 927803, 996019, 1034251, 1250309, 1285937, 2224063, 2281003, 2456191, 2607109, 2741561, 2773073, 3210353, 3336209, 4206817, 4403647, 4632161

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

23 is in the sequence because 23+29 (consecutive primes) = 52 = 18+34 (consecutive heptagonal numbers).

Mathematica

Module[{hep=Total/@Partition[PolygonalNumber[7, Range[1500]], 2, 1]}, Select[ Partition[Prime[Range[PrimePi[Max[hep]/2]]], 2, 1], MemberQ[hep, Total[#]]&]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 04 2019 *)

Prog

(PARI) L=List(); forprime(p=2, 6000000, q=nextprime(p+1); t=p+q; if(issquare(20*t-16, &sq) && (sq-2)%10==0, u=(sq-2)\10; listput(L, p))); Vec(L)
(Python)
from sympy import prevprime, nextprime
A298466_list, n, m = [], 1 , 8
while len(A298466_list) < 10000:
    k = prevprime(m//2)
    if k + nextprime(k) == m:
        A298466_list.append(k)
    n += 1
    m += 10*n-3 # Chai Wah Wu, Jan 19 2018

Crossrefs

Cf. A000040, A000566, A061275, A298462, A298463, A298464, A298465.

Sequence in context: A055326 A271851 A133338 * A358069 A116986 A271962

Adjacent sequences: A298463 A298464 A298465 * A298467 A298468 A298469

Keyword

nonn

Author

Colin Barker, Jan 19 2018

Status

approved