A295708 Numbers n such that prime(n) contains a substring of all the prime digits in order, i.e., "2357".

350, 8919, 13213, 15699, 18175, 19909, 20623, 20886, 20887, 20888, 20889, 20890, 20891, 20892, 21416, 27890, 30161, 30935, 32471, 43332, 43333, 43334, 46246, 47005, 48517, 52993, 53745, 57484, 64129, 65688, 70729, 71446, 72909, 72998, 73639, 77949, 80241, 80242

Offset

1,1

Comments

12941584 is the least integer m with more than one "2357" substring in prime(m).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ n. - Charles R Greathouse IV, Dec 28 2017

Example

8919 is in the sequence because prime(8919) = 92357 contains a substring of prime digits "2357".
27890 is in the sequence because prime(27980) = 323579 contains a substring of prime digits "2357".

Maple

F:= proc(d) local x, y, j;
  op(map(numtheory:-pi, sort(convert(select(isprime, {seq(seq(seq(x+10^j*2357+10^(j+4)*y, y=10^(d-j-5)..10^(d-j-4)-1), x=1..10^j-1, 2), j=1..d-5),
seq(10^(d-4)*2357+x, x=1..10^(d-4)-1), seq(10^4*x+2357, x=10^(d-5)..10^(d-4)-1)}), list))));
end proc:
350, seq(F(d), d=5..7); # Robert Israel, Nov 29 2017

Mathematica

Select[Range[100000], MemberQ[Partition[IntegerDigits[Prime[#]], 4, 1], {2, 3, 5, 7}] &]

Prog

(PARI) isok(n)=p = prime(n); ret = 0; while (p > 1, if ((p % 10000) == 2357, ret = 1; break); p = floor(p/10); ); return (ret); \\ Michel Marcus, Dec 15 2017

Crossrefs

Cf. A054261, A069489, A085823.

Sequence in context: A108776 A184609 A322668 * A232786 A084875 A364508

Adjacent sequences: A295705 A295706 A295707 * A295709 A295710 A295711

Keyword

nonn,base

Author

K. D. Bajpai, Nov 26 2017

Status

approved