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 A226153 Numbers n such that triangular(n) is an average of 4 consecutive primes. 3
 5, 10, 14, 15, 22, 34, 49, 54, 64, 66, 81, 93, 104, 116, 121, 122, 146, 154, 156, 180, 194, 221, 222, 236, 270, 299, 320, 332, 334, 337, 346, 360, 369, 371, 374, 387, 416, 417, 429, 435, 444, 472, 492, 498, 511, 520, 551, 556, 617, 622, 637, 654, 657, 670, 674, 677, 680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Zak Seidov, Table of n, a(n) for n = 1..3000 MAPLE A034963 := proc(n) add(ithprime(i), i=n..n+3) ; end proc: istriangular:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then return t1 ; else return -1; end if; end; for n from 1 to 90000 do s := A034963(n)/4 ; if type(s, 'integer') then tr := istriangular(s) ; if tr >= 0 then printf("%d, ", tr) ; end if; end if; end do: # R. J. Mathar, Jun 06 2013 MATHEMATICA Module[{nn=30000, ntrs, m}, ntrs=Table[{n, (n(n+1))/2}, {n, nn}]; m=Mean/@Partition[Prime[ Range[ nn]], 4, 1]; Select[ntrs, MemberQ[m, #[[2]]]&]][[;; , 1]] (* Harvey P. Dale, Jun 08 2023 *) PROG (C) #include #include #include #define TOP (1ULL<<30) int main() { unsigned long long i, j, p1, p2, p3, 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 (p3=2, p2=3, p1=5, i=7; i < TOP; i+=2) if ((c[i>>4] & (1<<((i>>1) & 7)))==0) { s = p3 + p2 + p1 + i; if (s%4==0) { s/=4; r = sqrt(s*2); if (r*(r+1)==s*2) printf("%llu, ", r); } p3 = p2, p2 = p1, p1 = i; } return 0; } CROSSREFS Cf. A102655, A226151. Sequence in context: A313451 A164889 A173553 * A275991 A313452 A023981 Adjacent sequences: A226150 A226151 A226152 * A226154 A226155 A226156 KEYWORD nonn AUTHOR Alex Ratushnyak, May 28 2013 STATUS approved

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Last modified April 21 06:29 EDT 2024. Contains 371850 sequences. (Running on oeis4.)