A178344 -id:A178344 - cp's OEIS frontend

A178562 First differences of A178344.

1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -10, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -3, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -18, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -3, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -11, 1, 1, 1

Offset: 0

Juri-Stepan Gerasimov, May 29 2010

Antti Karttunen, Table of n, a(n) for n = 0..65537

A178344(n) = if(!n,1,my(i=1, s=0); while(n, s+=prime(i)^(n%2); n >>= 1; i++); (s));
A178562(n) = (A178344(n+1)-A178344(n)); \\ Antti Karttunen, Sep 29 2018

a(n) = A178344(n+1) - A178344(n).

Two terms corrected by R. J. Mathar, May 31 2010

A178563 Primes p such that A178344(p) is also prime.

Original entry on oeis.org

3, 11, 37, 47, 59, 131, 149, 151, 157, 163, 181, 191, 193, 197, 229, 233, 239, 251, 523, 541, 547, 557, 569, 599, 601, 613, 617, 631, 643, 653, 661, 677, 701, 727, 751, 761, 769, 787, 809, 823, 839, 883, 937, 941, 947, 953, 967, 971, 1021

Offset: 1

Juri-Stepan Gerasimov, May 29 2010

nonn

			a(22)=601 because 29^1 + 23^0 + 19^0 + 17^1 + 13^0 + 11^1 + 7^1 + 5^0 + 3^0 + 2^1 = 71 is prime and 601 = 1001011001_2.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

A178344 := proc(n) local bdgs; bdgs := convert(n,base,2) ; add( ithprime(i)^op(i,bdgs), i=1..nops(bdgs)) ; end proc:
for n from 1 to 2000 do if isprime(n) and isprime(A178344(n)) then printf("%d,",n) ; end if; end do: # R. J. Mathar, Jun 07 2010

Select[Prime@ Range@ 200, PrimeQ@ Total@ MapIndexed[Prime[First@ #2]^#1 &, Reverse@ IntegerDigits[#, 2]] &] (* Michael De Vlieger, Feb 19 2019 *)

229, 233, 541 inserted by R. J. Mathar, Jun 07 2010

cp's OEIS Frontend

A178562 First differences of A178344.

Views

Author

Keywords

Links

Programs

PARI

Formula

Extensions