A147846 Triangular numbers n*(n+1)/2 with n or n+1 prime.

1, 3, 6, 10, 15, 21, 28, 55, 66, 78, 91, 136, 153, 171, 190, 253, 276, 406, 435, 465, 496, 666, 703, 820, 861, 903, 946, 1081, 1128, 1378, 1431, 1711, 1770, 1830, 1891, 2211, 2278, 2485, 2556, 2628, 2701, 3081, 3160, 3403, 3486, 3916, 4005, 4656, 4753, 5050

Offset: 1

Author

Giovanni Teofilatto, Nov 15 2008

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A034953, A008837.

Programs

PARI

lista(nn) = {for (n=1, nn, if (isprime(n) || isprime(n+1), print1(n*(n+1)/2, ", ")););} \\ Michel Marcus, Jun 03 2013

PARI

print1(1);forprime(p=3,7,print1(", "p*(p-1)/2", "p*(p+1)/2)) \\ Charles R Greathouse IV, Jun 03 2013

Formula

a(n) ~ (n^2 log^2 n)/8. - Charles R Greathouse IV, Jun 03 2013

A034953 UNION A008837. - R. J. Mathar, Jun 13 2025

Extensions

Missing terms 28=7*8/2, 91=13*14/2 etc. inserted by R. J. Mathar, Jan 30 2010