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 A226155 Smallest of four consecutive primes whose average is a triangular number. 0
 11, 47, 101, 109, 241, 587, 1217, 1481, 2069, 2203, 3313, 4357, 5443, 6779, 7351, 7489, 10723, 11927, 12239, 16267, 18911, 24517, 24733, 27953, 36571, 44839, 51347, 55249, 55931, 56941, 60017, 64951, 68239, 68993, 70117, 75041, 86719, 87133, 92227, 94819, 98773, 111611 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS MAPLE A000217inv:=proc(n) local t1; t1:=floor(sqrt(2*n)); if n = t1*(t1+1)/2 then return t1 ; else return -1; end if; end; isA226155 := proc(n) local p1, p2, p3, a102655 ; if isprime(n) then p1 := nextprime(n) ; p2 := nextprime(p1) ; p3 := nextprime(p2) ; a102655 := (n+p1+p2+p3)/4 ; if type(a102655, 'integer') then if A000217inv(a102655) >= 0 then return true; else return false; end if; else return false; end if; else false; end if; end proc: for n from 1 do p := ithprime(n) ; if isA226155(p) then printf("%d, \n", p) ; end if; end do: # R. J. Mathar, Jun 06 2013 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, ", p3); } p3 = p2, p2 = p1, p1 = i; } return 0; } CROSSREFS Cf. A102655, A226151 A226153, A226154. Sequence in context: A142103 A031910 A009941 * A107149 A158463 A143830 Adjacent sequences: A226152 A226153 A226154 * A226156 A226157 A226158 KEYWORD nonn AUTHOR Alex Ratushnyak, May 28 2013 STATUS approved

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Last modified March 26 13:22 EDT 2023. Contains 361549 sequences. (Running on oeis4.)