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A361744

A(n,k) is the least m such that there are k primes in the set {prime(n) + 2^i | 1 <= i <= m}, or -1 if no such number exists; square array A(n,k), n > 1, k >= 1, read by antidiagonals.

1, 2, 1, 3, 3, 2, 4, 5, 4, 1, 6, 11, 6, 3, 2, 7, 47, 8, 5, 4, 1, 12, 53, 10, 7, 8, 13, 2, 15, 141, 16, 9, 20, 21, 6, 3, 16, 143, 18, 15, 38, 33, 30, 7, 1, 18, 191, 20, 23, 64, 81, 162, 39, 3, 4, 28, 273, 28, 29, 80, 129, 654, 79, 5, 12, 2 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`2,2`
	LINKS	`Table of n, a(n) for n=2..67.`
	EXAMPLE	`p = prime(2) = 3, m=1, u = {p + 2^k \| 1 <= k <= m} = {5} contains one prime, and no lesser m satisfies this, so A(2,1) = 1.` `Square array A(n,k) n > 1 and k >= 1 begins:` `1, 2, 3, 4, 6, 7, 12, 15, 16, 18, ...` `1, 3, 5, 11, 47, 53, 141, 143, 191, 273, ...` `2, 4, 6, 8, 10, 16, 18, 20, 28, 30, ...` `1, 3, 5, 7, 9, 15, 23, 29, 31, 55, ...` `2, 4, 8, 20, 38, 64, 80, 292, 1132, 4108, ...` `1, 13, 21, 33, 81, 129, 285, 297, 769, 3381, ...` `2, 6, 30, 162, 654, 714, 1370, 1662, 1722, 2810, ...` `3, 7, 39, 79, 359, 451, 1031, 1039, 11311, 30227, ...` `1, 3, 5, 7, 9, 13, 15, 17, 23, 27, ...`
	PROG	`(PARI) A(n, k)= {my(nb=0, p=prime(n), m=1); while (nb<k, if (ispseudoprime(p+2^m), nb++); m++); m--}`
	CROSSREFS	`Cf. A057732 (1st row), A094076 (1st column).` `Cf. A361679.` `Cf. A019434 (primes 2^n+1), A057732 (2^n+3), A059242 (2^n+5), A057195 (2^n+7), A057196(2^n+9), A102633 (2^n+11), A102634 (2^n+13), A057197 (2^n+15), A057200 (2^n+17), A057221 (2^n+19), A057201 (2^n+21), A057203 (2^n+23).` `Cf. A205558 and A231232 (with 2k instead of 2^k).` `Sequence in context: A002347 A006642 A332435 A324751 A210595 A094435` `Adjacent sequences: A361741 A361742 A361743 * A361745 A361746 A361747`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Jean-Marc Rebert, Mar 22 2023`
	STATUS	`approved`

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Last modified September 8 14:54 EDT 2024. Contains 375753 sequences. (Running on oeis4.)