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A371757 Numbers of the form (4^(p^(k+1)) + 1)/(4^(p^k)) + 1), where k >= 1 and p is an odd prime other than 5. 1
4033, 68719214593, 19341632594266545643831297, 324518553658426708768757511094273, 1684996264962499703367587717863072443065045481313942556034056847361 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Mąkowski and Rotkiewicz (1969) proved that all the terms are Fermat pseudoprimes to base 2 (A001567).
The next term has 94 digits and is too large to include in the data section.
LINKS
Andrzej Mąkowski and Andrzej Rotkiewicz, On pseudoprime numbers of special form, Colloquium Mathematicum, Vol. 2, No. 20 (1969), pp. 269-271; alternative link.
Wikipedia, Pseudoprime.
MATHEMATICA
f[p_, k_] := (4^(p^(k + 1)) + 1)/(4^(p^k) + 1);
seq[max_] := Module[{s = {}, p = 3, f1, k, addFlag = True}, While[addFlag, If[p == 5, Continue[]]; k = 1; addFlag = False; While[(f1 = f[p, k]) < max, AppendTo[s, f1]; addFlag = True; k++]; p = NextPrime[p, If[p == 3, 2, 1]]]; Sort[s]]; seq[10^80]
CROSSREFS
Subsequence of A001567.
Sequence in context: A234834 A212601 A060896 * A206617 A252686 A178274
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 05 2024
STATUS
approved

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Last modified May 26 13:41 EDT 2024. Contains 372826 sequences. (Running on oeis4.)