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A127305
Primes p such that p + (sum of the prime factors of p-1) + (sum of prime factors of p+1) is prime.
2
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
Sequence in context: A359252 A176060 A168172 * A363753 A333519 A270294
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