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A226155
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Smallest of four consecutive primes whose average is a triangular number.
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0
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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
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..42.
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MAPLE
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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
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PROG
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(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, ", p3);
}
p3 = p2, p2 = p1, p1 = i;
}
return 0;
}
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CROSSREFS
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Cf. A102655, A226151 A226153, A226154.
Sequence in context: A142103 A031910 A009941 * A107149 A158463 A143830
Adjacent sequences: A226152 A226153 A226154 * A226156 A226157 A226158
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KEYWORD
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nonn
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AUTHOR
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Alex Ratushnyak, May 28 2013
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STATUS
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approved
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