A259564 Numbers n such that the sum of the prime factors (including repeats) of prime(n)-1 and prime(n+1)-1 are the same.

5, 7, 11, 30, 133, 160, 415, 527, 883, 1257, 2025, 2771, 2775, 6650, 6932, 13793, 19091, 30695, 32341, 33722, 36372, 37944, 40532, 42141, 47230, 60986, 77956, 82165, 90564, 111414, 113106, 136036, 147573, 148357, 158279, 169137, 169604, 171549, 174540, 187679

Offset: 1

Author

Otis Tweneboah, Pratik Koirala, Eugene Fiorini, Nathan Fox, Jun 30 2015

Keywords

• nonn

Comments

Although there are more terms than A105403 so far, these numbers are still fairly uncommon.

Is this sequence infinite?

Examples

			The prime factors of prime(30)-1 are 2,2,2,2,7 and the prime factors of prime(31)-1 are 2,3,3,7. The sum of entries in each of these lists is 15.
		

Crossrefs

Cf. A001414, A105403, A259562.

Programs

Mathematica

SequencePosition[Table[Total[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ p-1]]],{p,Prime[Range[200000]]}],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 12 2020 *)

PARI

spff(n) = {my(f=factor(n)); sum(k=1, #f~, f[k,1]*f[k,2]);}
lista(nn) = {forprime(p=2, nn, if (spff(p-1)==spff(nextprime(p+1)-1), print1(primepi(p), ", ")););} \\ Michel Marcus, Jun 30 2015

Extensions

More terms from Alois P. Heinz, Jun 30 2015

Name edited by Zak Seidov, Jul 02 2015