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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
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 <stdio.h>
#include <stdlib.h>
#include <math.h>
#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<TOP; j+=i) c[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
Sequence in context: A313451 A164889 A173553 * A275991 A313452 A023981
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.)