A175349 a(n) is the smallest positive integer that, when written in binary, contains the binary representations of both the n-th prime and the n-th composite as (possibly overlapping) substrings.

4, 6, 40, 39, 43, 108, 113, 79, 368, 466, 500, 149, 361, 344, 377, 53, 59, 988, 542, 2272, 2121, 1103, 2259, 356, 609, 1253, 3304, 3434, 876, 2929, 4078, 387, 393, 2226, 4787, 1687, 630, 2615, 1336, 5561, 2874, 5820, 382, 4033, 12608, 8391, 13506, 14276, 8931, 14662

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

The 7th prime is 17, which is 10001 in binary. The 7th composite is 14, which is 1110 in binary. The smallest positive integer that, when written in binary, contains these binary representations as substrings is 113, which is 1110001 in binary. a(7) = 113, therefore.

Mathematica

comp[n_] := FixedPoint[n + 1 + PrimePi[#] &, n + 1 + PrimePi[n]]; sub[n_, x_] := MemberQ[Partition[IntegerDigits[n, 2], IntegerLength[x, 2], 1],
IntegerDigits[x, 2]]; a[n_] := Block[{c = comp[n], p = Prime[n], k}, k = Max[p, c]; While[! sub[k, p] || ! sub[k, c], k++]; k]; Array[a, 50] (* Giovanni Resta, Jul 02 2018 *)

Crossrefs

Cf. A004676, A115454.

Sequence in context: A103234 A074061 A125081 * A281223 A023644 A319672

Adjacent sequences: A175346 A175347 A175348 * A175350 A175351 A175352

Keyword

base,nonn

Author

Leroy Quet, Apr 19 2010

Extensions

a(9)-a(50) from Giovanni Resta, Jul 02 2018

Status

approved