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 A226069 Primes p such that p-1 is a square and p-2 is a triangular number. 6
 2, 5, 17, 17957, 4726277, 23911673957 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Roots of squares: a(n)-1 = b(n)*b(n), b(n) = A226070(n). Roots of triangular numbers: a(n)-2 = c(n)*(c(n)+1)/2, c(n) = A226071(n). Primes of the form A006452(k)^2+1. a(7) is too large to include here (see b-file). - Max Alekseyev, Jan 30 2014 LINKS Max Alekseyev, Table of n, a(n) for n = 1..12 PROG (C) #include #include #include #define TOP (1ULL<<34) int main() {   unsigned long long i, j, k, r, n=1;   unsigned char *c = (unsigned char *)malloc(TOP/8);   memset(c, 0, TOP/8);   for (i=3; i < TOP*2; i+=2)     if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {       ++n;       if (i<(1ULL<<32))         for (j=i*i>>1; j>3] |= 1 << (j&7);     }   //printf("%llu\n", n);   for (i=1, j=i*i+1; j < TOP*2; i++, j=i*i+1)     if(j==2 || ((j&1) && (c[j>>4] & (1<<((j>>1) & 7)))==0)) {       k = j-2;       r = sqrt(k*2);       if (r*r+r==k*2) printf("%9llu %9llu %9llu\n", r, i, j);     }   free(c);   return 0; } CROSSREFS Cf. A226070-A226074. Sequence in context: A182313 A124374 A113617 * A258429 A117839 A269665 Adjacent sequences:  A226066 A226067 A226068 * A226070 A226071 A226072 KEYWORD nonn AUTHOR Alex Ratushnyak, May 25 2013 EXTENSIONS Terms a(7)-a(12) from Max Alekseyev, Jan 30 2014 STATUS approved

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Last modified September 30 11:32 EDT 2020. Contains 337439 sequences. (Running on oeis4.)