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 A226148 Smallest of three consecutive primes whose sum is a triangular number. 3
 2, 3, 619, 1123, 3373, 4603, 6829, 9067, 18973, 25933, 29179, 29741, 33211, 40583, 48313, 72923, 74923, 117991, 130973, 202201, 231067, 253993, 255217, 267317, 291491, 339139, 346309, 363829, 423191, 449621, 476279, 489337, 519487, 533713, 539093, 592507, 602603, 621133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..2300 MAPLE R:= 2: count:= 1: for k from 1 while count < 100 do for j from 1 to 2 do m:= 4*k+j; x:= m*(m+1)/2; q= prevprime(ceil(x/3)); p:= prevprime(q); r:= nextprime(q); t:= p+q+r; if t < x then while t < x do p:= q; q:= r; r:= nextprime(r); t:=p+q+r od elif t > x then while t > x do r:= q; q:= p; p:= prevprime(p); t:= p+q+r od fi; if t = x then R:= R, p; count:= count+1; fi od od : R; # Robert Israel, Oct 18 2021 PROG (C) #include #include #include #define TOP (1ULL<<30) int main() { unsigned long long i, j, p1, p2, r, s; unsigned char *c = (unsigned char *)malloc(TOP/8); memset(c, 0, TOP/8); for (i=3; i < TOP; i+=2) if ((c[i>>4] & (1<<((i>>1) & 7)))==0 /*&& i<(1ULL<<32)*/) for (j=i*i>>1; j>3] |= 1 << (j&7); for (p2=2, p1=3, i=5; i < TOP; i+=2) if ((c[i>>4] & (1<<((i>>1) & 7)))==0) { s = p2 + p1 + i; r = sqrt(s*2); if (r*(r+1)==s*2) printf("%llu, ", p2); p2 = p1, p1 = i; } return 0; } CROSSREFS Cf. A076304, A206279, A226145, A226146, A226147, A226149, A226150. Cf. A167788 (the resulting triangular numbers). Sequence in context: A240709 A264577 A165770 * A108332 A256115 A066685 Adjacent sequences: A226145 A226146 A226147 * A226149 A226150 A226151 KEYWORD nonn AUTHOR Alex Ratushnyak, May 28 2013 STATUS approved

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Last modified June 4 20:02 EDT 2023. Contains 363128 sequences. (Running on oeis4.)