A202262 Composite numbers in which all substrings are composite.

4, 6, 8, 9, 44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 94, 96, 98, 99, 444, 446, 448, 464, 466, 468, 469, 484, 486, 488, 494, 496, 498, 644, 646, 648, 649, 664, 666, 668, 669, 684, 686, 688, 694, 696, 698, 699, 844, 846, 848, 849, 864, 866, 868, 869, 884, 886

Offset: 1

Author

Jaroslav Krizek, Dec 25 2011

Keywords

• nonn
• base

Comments

Subsequence of A062115, A202260, A029581.

Supersequence of A202265.

This is a 10-automatic sequence, see A071062. - Charles R Greathouse IV, Jan 01 2012

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A202262
• Index entries for 10-automatic sequences

Crossrefs

Cf. A085823 (primes in which all substrings are primes), A068669 (noncomposite numbers in which all substrings are noncomposite), A062115 (nonprimes in which all substrings are nonprimes).

Cf. A010051.

Programs

Mathematica

sub[n_] := Block[{d = IntegerDigits[n]}, Union@ Reap[ Do[Sow@ FromDigits@ Take[d, {i, j}], {j, Length@ d}, {i, j}]][[2, 1]]]; Select[ Range@ 900, Union[{4, 6, 8, 9}, IntegerDigits[#]] == {4, 6, 8, 9} && AllTrue[sub[#], CompositeQ] &] (* Giovanni Resta, Dec 20 2019 *)

PARI

See Links section.

Extensions

Data corrected by Reinhard Zumkeller, May 05 2012

Data corrected by Rémy Sigrist, Dec 19 2019

Incorrect Haskell program deleted by M. F. Hasler, Dec 20 2019