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
Keywords
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000 (updated by _Robert Israel_, May 25 2022)
Programs
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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 */
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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
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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 *)
Extensions
Edited and extended by Klaus Brockhaus, Apr 06 2007
Edited by N. J. A. Sloane, May 25 2022
Comments