A281317 - OEIS

A281317

Primes p such that p == i mod d(i) where d(i) are the prime divisors of 2p+1.

7, 13, 37, 67, 157, 337, 367, 607, 787, 937, 1093, 3037, 3307, 7717, 9187, 12757, 15187, 19687, 27337, 35437, 42187, 49207, 69457, 75937, 267907, 347287, 683437, 744187, 797161, 882367, 1148437, 1458607, 1736437, 2067187, 2870437, 2929687, 3125587, 4823437

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OFFSET

1,1

COMMENTS

Subsequence of A053176.

a(n)== 1 mod 6 or a(n)== 1, 7 mod 12. A majority of members of the sequence are congruent to 7 mod 10.

omega(2*a(n)+1) = 1 for n = 2, 11, 29,... => 2*a(n)+1 = 3^3, 3^7, 3^13,... where omega(n) = A001221(n).

LINKS

Table of n, a(n) for n=1..38.

EXAMPLE

157 is in the sequence because 2*157 + 1 = 315 = 3 ^ 2 * 5 * 7 => 157 == 1 (mod 3), 157 == 2 (mod 5) and 157 == 3 (mod 7).

MAPLE

with(numtheory):

for n from 2 to 10^5 do:

p:=ithprime(n):q:=2*p+1:x:=factorset(q):n1:=nops(x):j:=0:

for i from 1 to n1 do:

if irem(p, x[i])=i

then j:=j+1:

else

fi:

od:

if j=n1

then

printf(`%d, `, p):

else

fi:

od:

MATHEMATICA

Select[Prime@ Range[10^6], Function[p, Function[i, Times @@ Boole@ MapIndexed[Mod[p, #1] == First@ #2 &, FactorInteger[i][[All, 1]]] > 0][2 p + 1]]] (* Michael De Vlieger, Jan 20 2017 *)

CROSSREFS

Cf. A001221, A053176, A053177.

Sequence in context: A155036 A088985 A022005 * A336773 A118819 A118525

Adjacent sequences: A281314 A281315 A281316 * A281318 A281319 A281320

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jan 20 2017

STATUS

approved