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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
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
Sequence in context: A293625 A084821 A345654 * A066763 A164788 A033849
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.)