

A175349


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


0



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
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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



