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URL: https://oeis.org/A259564

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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.
1
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
1,1
COMMENTS
Although there are more terms than A105403 so far, these numbers are still fairly uncommon.
Is this sequence infinite?
EXAMPLE
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.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
EXTENSIONS
More terms from Alois P. Heinz, Jun 30 2015
Name edited by Zak Seidov, Jul 02 2015
STATUS
approved