A118506 Smaller of two consecutive Sophie Germain primes with the same digital sum.

113, 491, 683, 743, 2549, 3539, 3803, 3911, 4019, 4373, 4391, 4409, 4481, 5081, 6113, 6173, 6563, 6581, 7103, 7433, 7823, 9419, 9539, 10091, 10163, 10253, 10313, 10691, 11813, 12329, 12653, 13049, 13463, 14009, 14081, 14159, 14303, 15629, 15773

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n)=A005384(k): A007953(A005384(k))=A007953(A005384(k+1)) for some k. - R. J. Mathar, Jun 02 2006

Example

113 is in the sequence because it is a Sophie Germain prime and the next Sophie Germain prime (namely 131) has the same digital sum.

Maple

isA005384 := proc(n) RETURN(isprime(n) and isprime(2*n+1) ) ; end : A007953 := proc(n) local t1, t2; t1 := n; t2 := 0; while t1 <> 0 do t2 := t2 + (t1 mod 10); t1 := floor(t1/10); od: t2; end: A118506 := proc(pmax) local resul, n, p, opri ; resul := [] ; opri := 0 ; for n from 1 to pmax do p := ithprime(n) ; if isA005384(p) then if A007953(p) = A007953(opri) then resul := [op(resul), opri] ; fi ; opri := p ; fi ; end : RETURN(resul) ; end: A118506(4000) ; # R. J. Mathar, Jun 02 2006

Mathematica

Transpose[Select[Partition[Select[Prime[Range[2000]], PrimeQ[ 2#+1]&], 2, 1], Total[ IntegerDigits[#[[1]]]]==Total[IntegerDigits[#[[2]]]]&]][[1]] (* Harvey P. Dale, Jun 01 2015 *)

Crossrefs

Cf. A005384.

Sequence in context: A353957 A142850 A203722 * A341230 A109563 A142024

Adjacent sequences: A118503 A118504 A118505 * A118507 A118508 A118509

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), May 06 2006

Extensions

More terms from R. J. Mathar, Jun 02 2006

Status

approved