A127305 Primes p such that p + (sum of the prime factors of p-1) + (sum of prime factors of p+1) is prime.

2, 13, 47, 71, 101, 151, 193, 239, 241, 293, 331, 337, 359, 383, 397, 401, 421, 463, 487, 557, 577, 709, 773, 797, 821, 929, 1019, 1031, 1069, 1093, 1103, 1181, 1217, 1249, 1327, 1367, 1423, 1499, 1571, 1759, 1787, 1789, 1831, 1871, 1877, 1913, 1933, 2053

Offset

1,1

Comments

The primes are taken "with multiplicity".

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000 (updated by Robert Israel, May 25 2022)

Example

2 is a term, since 2 + 0 + 3 = 5 is a prime.
13 is a term since 13 + (2+2+3) + (2+7) = 29 is prime, i.e. the prime factors are added with multiplicity.
151 is prime, 150 = 2*3*5*5, 152 = 2*2*2*19. 151 + 2+3+5+5 + 2+2+2+19 = 191 is prime, hence 151 is a term.

Maple

spf:= proc(n) local t; add(t[1]*t[2], t = ifactors(n)[2]) end proc:
filter:= proc(p) isprime(p) and isprime(p+spf(p-1)+spf(p+1)) end proc:
select(filter, [$2..10000]); # Robert Israel, May 25 2022

Mathematica

pspfQ[n_] := PrimeQ[n + Total[Flatten[Table[#[[1]], {#[[2]]}] & /@ Flatten[FactorInteger[n + {1, -1}], 1] ] ] ]; {2}~Join~Select[Prime[Range[400]], pspfQ] (* Harvey P. Dale, Jan 08 2015, corrected by Michael De Vlieger, May 25 2022 *)

Prog

(Magma) [ p: p in PrimesInInterval(3, 2100) | IsPrime(&+[ &+[ k[1]*k[2]: k in Factorization(n)]: n in [p-1..p+1] ] ) ]; /* Klaus Brockhaus, Apr 06 2007 */

Crossrefs

Cf. A210934, A210936.

Sequence in context: A359252 A176060 A168172 * A363753 A333519 A270294

Adjacent sequences: A127302 A127303 A127304 * A127306 A127307 A127308

Keyword

nonn

Author

J. M. Bergot, Mar 28 2007

Extensions

Edited and extended by Klaus Brockhaus, Apr 06 2007

Edited by N. J. A. Sloane, May 25 2022

Status

approved