A105888 a(n) = the smallest prime that, when written in binary, ends with the substring of 2n-1 in binary.

3, 3, 5, 7, 41, 11, 13, 31, 17, 19, 53, 23, 89, 59, 29, 31, 97, 163, 37, 103, 41, 43, 109, 47, 113, 179, 53, 311, 313, 59, 61, 127, 193, 67, 197, 71, 73, 331, 461, 79, 337, 83, 853, 599, 89, 347, 349, 223, 97, 227, 101, 103, 233, 107, 109, 239, 113, 499, 373, 503, 761

Offset: 1

Author

Leroy Quet, Aug 08 2009

Keywords

• base
• nonn

Examples

			2*5-1 = 9 is 1001 in binary. Looking at the binary numbers that end with 1001: 1001 = 9 in decimal is composite; 11001 = 25 in decimal is composite. But 101001 = 41 in decimal is prime. So a(5) = 41. - Corrected by _Rémy Sigrist_, Feb 05 2020
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192

Crossrefs

Cf. A164022.

Programs

Maple

isA105888 := proc(p,n) local pdgs,n21dgs ; pdgs := convert(p,base,2) ; n21dgs := convert(2*n-1,base,2) ; if nops(n21dgs) > nops(pdgs) then return false; else verify( [op(1..nops(n21dgs),n21dgs)],[op(1..nops(n21dgs),pdgs)],'sublist') ; end if; end proc: A105888 := proc(n) p := 2 ; while not isA105888(p,n) do p := nextprime(p) ; end do ; p ; end proc: seq(A105888(n),n=1..80) ; # R. J. Mathar, Dec 06 2009

Mathematica

pr=-16; Select[Prime[Range[200]], MultiplicativeOrder[pr, # ] == #-1 &]

PARI

a(n) = my (m=2*n-1); forstep (p=m, oo, 2^#binary(m), if (isprime(p), return (p)))

Extensions

Extended beyond a(10) by R. J. Mathar, Dec 06 2009