A298974 - OEIS

A298974

Lexicographic first sequence of positive integers such that a(n)*a(n+1) has a digit 4, and no term occurs twice.

1, 4, 6, 7, 2, 12, 17, 20, 21, 14, 3, 8, 5, 9, 16, 15, 23, 18, 13, 11, 22, 19, 24, 10, 34, 26, 29, 36, 39, 32, 27, 35, 40, 31, 37, 38, 28, 30, 47, 42, 44, 33, 43, 48, 50, 49, 46, 51, 54, 41, 45, 52, 57, 25, 56, 58, 53, 65, 62, 55, 59, 60, 64, 61, 63, 66, 67, 68, 69, 70, 71, 74, 73, 75, 72, 76, 79, 82, 77, 84, 81, 80, 78, 83, 88, 85, 97, 86, 87

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OFFSET

1,2

COMMENTS

A permutation of the positive integers.

LINKS

Table of n, a(n) for n=1..89.

EXAMPLE

a(1) = 1 is the least positive integer, and a(1) has no other constraint to satisfy.

a(2) = 4 is the least positive integer > a(1) = 1 such that a(2)*a(1) = 4 has a digit 4.

a(3) = 6 is the least positive integer not in {1, 4} such that a(3)*a(2) (= 24) has a digit 4: The smaller choices 2, 3 and 5 do not satisfy this.

a(4) = 7 is the least positive integer not in {1, 4, 6} such that a(4)*a(3) (= 42) has a digit 4: All available smaller choices do not satisfy this.

PROG

(PARI) A298974(n, f=1, d=4, a=1, u=[a])={for(n=2, n, f&&if(f==1, print1(a", "), write(f, n-1, " "a)); for(k=u[1]+1, oo, setsearch(u, k)&&next; setsearch(Set(digits(a*k)), d)&&(a=k)&&break); u=setunion(u, [a]); while(#u>1&&u[2]==u[1]+1, u=u[^1])); a}

CROSSREFS

Cf. A299402, A299403, A298975, ..., A298979: analog with digit 2, 3; ..., 9.

Cf. A299957, A299969, ..., A299988 (analog with addition instead of multiplication, and different digits).

Sequence in context: A135798 A197010 A021218 * A344983 A237515 A200939

Adjacent sequences: A298971 A298972 A298973 * A298975 A298976 A298977

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Feb 22 2018

STATUS

approved