A211162 -id:A211162 - cp's OEIS frontend

A211169 The least n-almost Sophie Germain prime.

2, 4, 52, 40, 688, 4900, 63112, 178240, 38272, 5357056, 1997824, 247221760, 586504192, 707436544, 15582115840, 47145459712, 77620412416, 1871289057280, 17787921498112, 10891875057664, 146305150615552, 535618317844480, 15921951753109504, 39754688251297792

Offset: 1

Don Reble, Paolo P. Lava, and Robert G. Wilson v, Jan 31 2013

nonn

			a(1)=2 because 2 and 5 are primes (A000040),
a(2)=4 because 4 and 9 are semiprimes (A001358),
a(3)=52 because the pair, 52 and 105, are 3-almost primes (A014612) and they are the least such pair,
a(4)=40 because the pair, 40 and 81, are 4-almost primes (A014613) and they are the least such pair, etc.

Cf. A005384 (Sophie Germain primes), A111153 (Sophie Germain semiprimes), A111173 (Sophie Germain 3-almost primes), A111176 (Sophie Germain 4-almost primes), A211162 (Sophie Germain 5-almost primes).

with(numtheory);
A211169:=proc(q)
local a,b,c,d,g,f,i,j,n;
for j from 1 to q do for n from 1 to q do
    a:=ifactors(n)[2]; b:=nops(a); c:=ifactors(2*n+1)[2]; d:=nops(c); g:=0; f:=0;
    for i from 1 to b do g:=g+a[i][2]; od; for i from 1 to d do f:=f+c[i][2]; od;
    if g=f and g=j then print(n); break;
fi; od; od; end:
A211169(1000000000000);

t = Table[0, {20}]; k = 2; While[k < 2700000001, x = PrimeOmega[k]; If[ t[[x]] == 0 && PrimeOmega[ 2k + 1] == x, t[[x]] = k; Print[{x, k}]]; k++]; t

a(15)-a(24) from Giovanni Resta, Jan 31 2013

A238257 Numbers n such that n and 2n+1 use only odd decimal digits.

Original entry on oeis.org

1, 3, 5, 7, 9, 15, 17, 19, 35, 37, 39, 55, 57, 59, 75, 77, 79, 95, 97, 99, 155, 157, 159, 175, 177, 179, 195, 197, 199, 355, 357, 359, 375, 377, 379, 395, 397, 399, 555, 557, 559, 575, 577, 579, 595, 597, 599, 755, 757, 759, 775, 777, 779, 795, 797, 799, 955, 957, 959, 975, 977, 979, 995, 997, 999, 1555, 1557, 1559, 1575, 1577, 1579

Offset: 1

Zak Seidov, Feb 21 2014

Sophie-Germain-analog for numbers with odd digits.

Also numbers with the first digit an odd digit and the other digits in {5, 7, 9}. - David A. Corneth, May 15 2018

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

Cf. A005384, A111153, A211162, A111173, A111176.

Select[Range[1600],AllTrue[Join[IntegerDigits[#],IntegerDigits[ 2#+1]], OddQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 15 2018 *)

is(n)=#setminus(setunion(Set(digits(n)),Set(digits(2*n+1))), [1,3,5,7,9])==0 \\ Charles R Greathouse IV, May 15 2018

a(5(3^k-1)/2) = 10^k-1. - Giovanni Resta, Feb 22 2014

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A211169 The least n-almost Sophie Germain prime.

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A238257 Numbers n such that n and 2n+1 use only odd decimal digits.

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