A339867 Primes p such that p + sigma(p-1) and p + sigma(p+1) are both prime.

13, 23, 41, 43, 53, 59, 61, 67, 131, 167, 193, 227, 263, 271, 283, 293, 311, 313, 397, 503, 523, 563, 571, 599, 607, 631, 653, 661, 701, 743, 827, 839, 907, 911, 919, 941, 947, 1031, 1087, 1103, 1171, 1181, 1187, 1301, 1319, 1321, 1381, 1499, 1531, 1559, 1619, 1621, 1663, 1741, 1747, 1811, 1847

Offset

1,1

Comments

Terms with sigma(p-1) = sigma(p+1) include 919, 334541 and 463219.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 41 is a term because 41 is prime, 41 + sigma(40) = 41+1+2+4+5+8+10+20+40=131 is prime, and 41 + sigma(42) = 41+1+2+3+6+7+14+21+42=137 is prime.

Maple

select(t -> isprime(t + numtheory:-sigma(t-1)) and isprime(t + numtheory:-sigma(t+1)), [seq(ithprime(i), i=1..300)])

Crossrefs

Cf. A339862, A000203.

Sequence in context: A164494 A164407 A259216 * A135283 A225519 A213655

Adjacent sequences: A339864 A339865 A339866 * A339868 A339869 A339870

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 19 2020

Status

approved