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 A298462 The first of two consecutive triangular numbers the sum of which is equal to the sum of two consecutive prime numbers. 5
 15, 45, 66, 276, 861, 1128, 1891, 2556, 3486, 4005, 5995, 7140, 7381, 15051, 20706, 21528, 24090, 26796, 28680, 34716, 46665, 52975, 56280, 69006, 74305, 83028, 83845, 98346, 102831, 103740, 109278, 110215, 112101, 135981, 148785, 150975, 176121, 179700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 45 is in the sequence because 45+55 (consecutive triangular numbers) = 100 = 47+53 (consecutive primes). MAPLE f:= proc(n) local p, q; p:= prevprime(floor((n+1)^2/2)); q:= nextprime(p); if p+q = (n+1)^2 then n*(n+1)/2 else NULL fi end proc: map(f, [\$2..1000]); # Robert Israel, Jan 19 2018 PROG (PARI) L=List(); forprime(p=2, 200000, q=nextprime(p+1); t=p+q; if(issquare(4*t, &sq) && (sq-2)%2==0, u=(sq-2)\2; listput(L, u*(u+1)/2))); Vec(L) CROSSREFS Cf. A000040, A000217, A061275, A298463, A298464, A298465, A298466. Sequence in context: A293625 A084821 A345654 * A066763 A164788 A033849 Adjacent sequences: A298459 A298460 A298461 * A298463 A298464 A298465 KEYWORD nonn AUTHOR Colin Barker, Jan 19 2018 STATUS approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)